We present a study of $B$-parameters for generic $Delta S=2$ four-quark operators in domain wall QCD. Our calculation covers all the $B$-parameters required to study the neutral kaon mixing in the standard model (SM) and beyond it. We evaluate one-loop renormalization factors of the operators employing the plaquette and Iwasaki gauge actions. Numerical simulations are carried out in quenched QCD with both gauge actions on $16^3times 32times 16$ and $24^3times 32times 16$ at the lattice spacing $1/aapprox 2$GeV. We investigate the relative magnitudes of the non-SM $B$-parameters to the SM one, which are compared with the previous results obtained with the overlap and the clover quark actions.
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